The classical Hall effect [1]}, [2]} is usually described by the local transport equations for the charge carriers that takes into account the effect of the Laplace-Lorentz force generated by a static magnetic field. Typically, in a planar Hall device, an electric generator imposes a constant electric current \(J_x^0\)  along the \(x\)  direction (see Fig.REF ), and the Hall voltage is then measured transversally along the \(y\)  direction at stationary regime, as a function of the magnetic field. The physical mechanisms behind this effect and the corresponding transport equations are well-known and are described in all reference textbooks. At stationary state under a perpendicular magnetic field, the Hall voltage can be measured, which is due to the accumulation of electric charges between the two edges of the Hall-bar. This state corresponds to a vanishing transverse current - or Hall current - \(J_y = 0\)  along the \(y\)  axis [3]}, [4]}. Indeed, the accumulation of electric charges at the edges produces a transverse electric field \(E_y\)  that balances the Lorentz force, so that the system reaches an “equilibrium” along the \(y\)  axis.
